1. Field of the Invention
The present invention relates to a lumped-element transmission line, and more particularly, to a lumped-element transmission line realized in multi-layered substrate.
2. Description of the Prior Art
Transmission lines are widely used as building blocks in RF and microwave circuit designs. For example, transmission lines of quarter-wavelength long are often used as impedance transformers, or to create effective open- or short-circuits in RF circuits. However, the required physical lengths of these transmission lines are often quite long, such that they will occupy large circuit areas especially for low frequency applications.
Conventionally, size reduction of transmission lines is accomplished by using meander line structures. Please refer to FIG. 1. FIG. 1 is a diagram of a prior art meander line structured transmission line with two ports P11 and P12. Utilizing the meander line structure reduces the size of the required transmission line, but the resulting circuit area is still too large for the requirements of modern wireless handheld devices. Alternatively, lumped-element realizations of transmission line may be employed. Please refer to FIG. 2 and FIG. 3. FIG. 2 is a diagram of a prior art T-equivalent circuit of a transmission line and FIG. 3 is a diagram of a prior art π-equivalent circuit of a transmission line. L21, L22, and L31 are inductors and C21, C31, and C32 are capacitors. P21 and P22, and P31 and P32 are ports of the transmission lines in FIG. 2 and FIG. 3 respectively. The circuits in FIG. 2 and FIG. 3 are accomplished by using lumped inductors and capacitors to realize the T- and π-equivalent circuits of transmission lines to reduce circuit size. FIG. 4 is a diagram of frequency response of a prior art T- or π-equivalent circuit of a transmission line compared to that of an ideal transmission line. In FIG. 4, the transverse axis represents frequency, and the vertical axis represents amplitude in dB. S11A and S21A are the reflection coefficient and transmission coefficient of an ideal transmission line, and S11B4 and S21B4 are the typical reflection coefficient and transmission coefficient of prior art T- or π-equivalent circuits of transmission lines. As shown in FIG. 4, these equivalent circuit models may only be considered as equivalents to ideal transmission lines in a very narrow bandwidth around the center frequency f0 as the deviations in transmission and reflection coefficients at frequencies away from f0 are quite large. For example, the difference between S21A and S21B4 at f1 is as large as d4 on the frequency response chart. In addition, the transmission coefficients for T- and π-equivalent circuits of transmission lines decrease rapidly above f0. These limit the usage of these equivalent-circuit models to narrow band applications. However, most recent RF systems occupy a wide frequency bandwidth and require wide-band circuit elements to keep favorable characteristics in the whole frequency band. Moreover, for multi-band RF communication systems, it is also required that the transmission line equivalent be operated at multiple frequencies.
There have been many approaches to try to solve the aforementioned problem but the improvement is limited. In addition, the poor frequency response of conventional lumped-element transmission line implementations becomes one of the thresholds in developing wide frequency band RF circuits.